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polygon problem in 3D

  • To: mathgroup at
  • Subject: polygon problem in 3D
  • From: James King <king at>
  • Date: Thu, 21 May 92 10:26:25 -0700

I have encountered what seems to be a bug when using
Polygon in 3D-graphics.  I am running Mathematica 2.03
Enhanced on a Mac IIci.

The problem is that if a polygon is viewed "edge-on", 
Mathematica gives a Postscript error message instead
of rendering the graphic.

For example,

tri3 = { {1,0,0}, {1, 1, 1}, {-2, -1, -1}}

gtri3 = Graphics3D[Polygon[tri3]]
Show[gtri3, ViewPoint->{2,1,2}]

draws a triangle in 3-space but if we change the viewpoint,

Show[gtri3, ViewPoint->{2,1,1}]

instead of drawing a line or nothing, this will 
produce this message: 

	The PostScript text in this cell did not contain 
	any drawing commands, or contained an error before
	the first valid drawing command.

The same message results, if the Graphics3D object consists
of this triangle along with another triangle in general 

In contrast, with 2D graphics, there is no error is one uses 
Polygon to draw a triangle made of 3 points which happen to 
be collinear.

This 3D bug is a problem if you deliberately want to show
a figure with some flat piece edge-on or if you happen to 
create such a view by varying some parameter when creating
an animation.

Can anyone suggest a convenient work-around (or is this fixed
in some newer version of Mathematica?

James King

Dept of Math GN-50
University of Washington
Seattle, WA 98195

king at

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